SYMPOSIA PAPER Published: 01 January 1974

Application of the J-lntegral to Obtain Some Similarity Relations


Experimental evidence seems to suggest that, for two elastic-plastic bodies which are geometrically similar to each other but with the same thickness and subjected to similar loadings, the ratio of their total energy inputs until the time of crack initiation is approximately equal to the ratio of their linear dimensions, independent of the amount of work hardening to be associated with the material. This result, as well as a set of other similarity conditions, is examined analytically in the present work from the J-integral criterion. It is shown that the similarity result in energy is exactly correct for rigidly plastic material as a consequence of Ilyushin's principle in plasticity. For the elastic-plastic material, if the two similar specimens are not extremely different in size, it can be justified for regions both close to and far from the crack tip. Under this condition, the ratio of their total energy inputs until the time of crack initiation will not be significantly influenced by the contributions from their transition regions and this similarity relation in energy may be a close approximation.

Author Information

Chang, SJ
Oak Ridge Laboratory, Oak Ridge, Tenn.
Witt, FJ
Westinghouse Electric Corporation, Madison, Pa.
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Developed by Committee: E08
Pages: 226–239
DOI: 10.1520/STP33143S
ISBN-EB: 978-0-8031-4645-7
ISBN-13: 978-0-8031-0361-0